The area of the region under the curve of a function f(x) = ax + b on the interval [0, 4] is 16 square units.
(a, b) ≠
Answers
Answer:
[tex](a,b) \ne (7,-9)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = ax + b[/tex]
[tex]Interval = [0,4][/tex]
[tex]Area = 16[/tex]
Required
[tex]a, b \ne[/tex]
The area is calculated as:
[tex]Area = \int\limits^a_b {f(x)} \, dx[/tex]
So, we have:
[tex]Area = \int\limits^4_0 {(ax + b)} \, dx[/tex]
Integrate
[tex]Area = (\frac{ax^2}{2} + bx)|\limits^4_0[/tex]
Expand
[tex]Area = [(\frac{a*4^2}{2} + b*4)] - [(\frac{a*0^2}{2} + b*0)][/tex]
[tex]Area = [(\frac{a*4^2}{2} + b*4)][/tex]
[tex]Area = 8a+ 4b[/tex]
This gives:
[tex]8a + 4b = 16[/tex]
Divide through by 4
[tex]2a + b = 4[/tex]
From the list of options, the possible values of a and b are:
[tex](a,b) = (-2,8) \to 2 * -2 + 8 = 4[/tex]
[tex](a,b) = (1,2) \to 2 * 1 + 2 = 4[/tex]
[tex](a,b) = (3,-2) \to 2 * 3 -2 = 4[/tex]
[tex](a,b) = (5,-6) \to 2 * 5 -6 = 4[/tex]
The odd one is:
[tex](a,b) = (7,-9) \to 2 * 7 -9 = 5[/tex]
Hence:
[tex](a,b) \ne (7,-9)[/tex]
![The Area Of The Region Under The Curve Of A Function F(x) = Ax + B On The Interval [0, 4] Is 16 Square](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/dFRAZqbVqpfo1KZJaNxPYKJLrJozxL0v.png)
Related Questions
Please help! find the common ratio of the geometric sequence. -1/4, 1/16, -1/64, 1/256,... A. 1/64 B. -1/4 C. -1/16 D. 1/16 E. 1/4
Answers
Answer:
B -1/4
Step-by-step explanation:
To find the common ratio, divide any term by the previous term.
1/16 ÷ -1/4 = 1/16 * -4 = -4/16 = -1/4
=====================================================
Explanation:
Pick any term of the sequence that isn't the first term. Divide whatever you picked by the previous term. That will compute the common ratio. This applies to geometric sequences only.
So let's say we pick on term 3 and divide it over term 2. That will get us...
[tex]r = \left(\text{3rd term}\right) \div \left(\text{2nd term}\right)\\\\r = -\frac{1}{64} \div \frac{1}{16}\\\\r = -\frac{1}{64} \times \frac{16}{1}\\\\r = \frac{-1*16}{64*1}\\\\r = -\frac{16}{64}\\\\r = -\frac{16}{16*4}\\\\r = -\frac{1}{4}\\\\[/tex]
Where r is the common ratio.
As another example, let's say we picked on term 4 and divided it over the third term
[tex]r = \left(\text{4th term}\right) \div \left(\text{3rd term}\right)\\\\r = \frac{1}{256} \div -\frac{1}{64}\\\\r = \frac{1}{256} \times -\frac{64}{1}\\\\r = \frac{1*(-64)}{256*1}\\\\r = -\frac{64}{256}\\\\r = -\frac{64}{64*4}\\\\r = -\frac{1}{4}\\\\[/tex]
We get the same result. I'll let you try dividing the second term over the first term. You should get r = -1/4 after simplifying.
-------------
Because the common ratio is r = -1/4, this means that we multiply each term by the common ratio to generate the next term.
For instance,
term 3 = (term 2)*(common ratio)
term 3 = (1/16)*(-1/4)
term 3 = -1/64
which matches with the given sequence
You enter a lottery. You pick three numbers
between 1 and 50. You win the grand prize if your
three numbers are picked. What is the probability
you win?
Answers
The ratio of kings to Queens was 4 to 5 if there 16 king how many queens were there
Answers
Answer:
20 Queens
Step-by-step explanation:
4:5
8:10
12:15
16:20
or
4:5 = 1:1.25
1.25 x 5 = 20
I hope this helps! ^_^
Eight people were asked what the balance of their checking account at the beginning of this past week was and how much it increased or decreased by the end of the week.
Create a scatter plot that represents the data that is shown in the table. The x-axis represents the beginning balance in thousands of dollars and the y-axis represents the change in the checking account in hundreds of dollars.
Name
Beginning balance
(in thousands of dollars)
Change in checking account
(in hundreds of dollars)
Billy 6 6
Barbara 4 5
Eli 3 2
Ken 1 5
Lara 8 4
Lindsey 3 8
Marie 4 2
Eduardo 5 3
Answers
Answer:
:D
Step-by-step explanation:
:DDDD
crikey expression to show whether it is equivalent to 3 * 9 or to 2x3x9
Answers
Answer:
See the matching below
Step-by-step explanation:
Given data
We have two expressions to match
3 * 9 and 2x3x9
3 * 9= 9*3
3 * 9=3*(4+5)
2x3x9= (2*3)*9
2x3x9= 9*3*2
My favorite bagel shop has 12 types of bagels, 10 types of cream cheese, and can choose to have it toasted or not . How many different bagels can order?
Answers
Answer: 240
Step-by-step explanation:
Given
Shop has 12 types of bagels, 10 types of cream and a option for roast
For making a bagel there are 12 choices to select a bagel, following this there are 10 choices for cream with a option to roast
So, total no different bagels that can be made out of the given is
[tex]\Rightarrow 12\times 10\times 2\\\Rightarrow 240\ \text{types}[/tex]
A 4-cup bottle of shampoo costs $24.84. What is the price per pint?
Answers
Type the missing number that makes these fractions equal:?/84=18/28
Answers
Answer:
la respuesta es 54/84
Step-by-step explanation:
54/84=0,642857
18/28=0.642857
Tom made the box plots to compare the number of calories between his morning snacks and his afternoon snacks.
Select from the drop-down menu to correctly complete the statement.
The range of calories in Tom’s morning snacks is about ______ ______ the range of calories in his afternoon snacks.
Answer Choices:
a). 25 a). less than
b). 60 b). more than
c). 100
d). 125
Answers
Answer:
80 less than
Step-by-step explanation:
A hose is used to fill an empty wading pool. The graph shows volume (in gallons) in the pool as a function of time (in minutes). Which of the following defines a formula for computing the time, 1, as a function of the volume, v?
Answers
What is the factorization of the polynomial below?
x2 + 11x + 10
A. (x + 2)(x + 5)
B. (x + 10)(x+ 1)
O C. (x+3)(x+3)
O D. (x + 5)(x+6)
HELP ASAP
Answers
Answer:
[tex]b. (x + 10)(x + 1)[/tex]
[tex] {x}^{2} + 11x + 10[/tex]
[tex]x(x + 10) + x + 10[/tex]
factor out x from the expression
[tex]x(x + 10) + x + 10[/tex]
factor out x +10 from the expression
[tex](x + 10)(x + 1)[/tex]
then its the answer
i hopenit helps , even though it was just my.....own opinion .....answer
Jason used the commutative property to write an expression that is equivalent to 3 4 + 5.6b + 9. 3 4 + 5.6b + 9 is equivalent to 9.0 + 56b + 3.4. Is Jason’s work correct?
Answers
Answer:
Yes, Jason's work is correct.
Step-by-step explanation:
When you use the commutative property, you can swap the numbers position and still get the same answer.
Hope this helps!!
Answer:
The answer is A No, he changed the terms
Step-by-step explanation:
The area of a rectangle is 96 square kilometers. Its width is 4 km less than its length.
Find its dimensions.
(please no links)
Answers
12x8=96
HELP ASAP!!.
50/5+2- [3+9] -3+7
Please show work
Answers
Answer:
4
Step-by-step explanation:
50/5+2-[3+9]-3+7
=10+2-12-3+7
=12-12-3+7
=-3+7
=4
Answer:
the correct answer is 4
Step-by-step explanation:
first your going to calculate the parentheses
[3+9]=12
which leaves the equastion as
50/5+2-12-3+7
then multiply and divide going left-right
50/5=10
which makes the equastion
10+2-12-3+7
then add and subtract going left to right so it would be
10+2=12-12=0-3=-3+7=4
X
Pema's bedroom is 18 feet long and 14 feet wide. She drew the plan below to
divide the room into sections. Which shows how to find the area of the Study
Corner?
1) 7 ft + 4 ft = 11 sq ft
11 ft
7 ft
10 ft + 7 ft = 17 sq ft
10 ft
Bed
Study
Corner
1) 10 ft x 7 ft
70 S
sq ft
4 ft Play Area Closet
1) 4 ft x 7 ft = 28 sq ft
Answers
70ft is the answer I think
In a free enterprise economy, who controls society and resources?
Answers
Answer:
Free enterprise, also known as free market or capitalism, is an economic system driven by supply and demand. Private businesses and consumers control the marketplace with little to no interference from the government. In this type of system, the government does not have a central plan for the nation's economy.
Step-by-step explanation:
does anybody know vertex form pls help
Answers
Answer:
9. y=(x+1)^2+4
10. y=(x-1)^2+4
7. (6,1)
8. (5,-2)
How do I find the indicated value?
Answers
Step-by-step explanation:
using this
t_n = a+ (n-1)d
Find the value of x, (x-7)°(2x+1) °
Pleas help!!!!
Answers
Answer:
x = 32
Step-by-step explanation:
2x+1 + x-7 = 90
3x - 6 = 90
3x = 96
x = 32
Pls, help me with this question
Answers
Answer:
37.5
Step-by-step explanation:
∠ABC (x) is an inscribed angle with arc AC being the arc it intercepts
An inscribed angle is equal to half the measure of its intercepted arc.
If arc AC = 75
Then x = [tex]75\frac{1}{2}[/tex]
75 / 2 = 37.5
Hence, x = 37.5
37.5 :)
PLZ HELP ME PLZ PLZ WILL MARK AS BRAINLIESTT!!!
Answers
A unit rate is a special type of ratio (also called a single-unit rate). It will compare 1 unit of some quantity to a different number of units of a different quantity. Unit rates are often used in real life situations, like when you need to convert between measurement systems.
I need to find the value of x
Answers
Answer:
15°
Step-by-step explanation:
x= 89-44-30= 15°
:))
You are going to Store E and your friend is going to Store F. Where on line n should you park to minimize the
distance you both will walk?
a. point Y
b. point G
c. point P
d. point 1
Answers
The table represents an exponential function.
What is the multiplicative rate of change of the
function?
х
1
2
y
2
2
5
2
25
2
125
3
4
02
05
Answers
Answer:
1/5
Step-by-step explanation:
correct on edg :)
An exponential function is a nonlinear function
The multiplicative rate of change of the function is 1/5
From the table, we have the following ordered pairs
(x,y) = (1,2) and (2,2/5)
Divide the y values, to calculate the rate (r)
[tex]r = \frac 25 \div 2[/tex]
This gives
[tex]r = \frac 15[/tex]
Hence, the multiplicative rate of change of the function is 1/5
Read more about exponential functions at:
https://brainly.com/question/11464095
choose all of the points that are solutions to y<3x+2:
A. (0,0)
B. (0,2)
C. (1,4)
D. (1,7)
E. (2,6)
F. (2,8)
Answers
Answer:
ACEStep-by-step explanation:
✓ A. (0, 0) [y < 3x + 2 → 0 < 2]
× B. (0, 2) [y < 3x + 2 → 2 < 2]
✓ C. (1, 4) [y < 3x + 2 → 4 < 5]
× D. (1, 7) [y < 3x + 2 → 7 < 5]
✓ E. (2, 6) [y < 3x + 2 → 6 < 8]
× F. (2, 8) [y < 3x + 2 → 8 < 8]
what is the meaning of equations
Answers
Answer:
I hope it helps u
Step-by-step explanation:
In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol(=) between two algebraic expressions that have the same value. ... In an algebraic equation, the left-hand side is equal to the right-hand side.
Mark me as brainlist answer,
have a nice day,
thank you
Given the graph below, locate the points of the reflection over the x-axis.
Answers
Answer:
Answer:
A: (1,3)
A': (1,-3)
---
B: (5,1)
B': (5,-1)
---
C: (-2,2)
C': (-2,-2)
---
D: (-5,4)
D': (-5,-4)
The reflection of the given points over the x-axis is:
(-5, -4), (-2, -2), (1, -3), (5, -1)
What is Coordinate Geometry?By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related.
As per the given data:
We are given a graph, and we have to find the reflection of the points in the graph over the y-axis.
From the graph given, the points are as as follows:
Let's assume the points as A, B, C and D
A = (-5, 4)
B = (-2, 2)
C = (1, 3)
D = (5, 1)
The reflection over the x-axis are as follows:
A' = (-5, -4)
B' = (-2, -2)
C' = (1, -3)
D' = (5, -1)
Hence, the reflection of the given points over the x-axis is:
(-5, -4), (-2, -2), (1, -3), (5, -1)
To learn more about Coordinate Geometry, click:
brainly.com/question/7869125
#SPJ3
An aquarium has the dimensions shown in the net below. What is the surface area of the aquarium?
A. 27 Square Feet
B.45 Square Feet
C. 28.5 Square Feet
D. 57 Square feet
(the top of the rectangle is 2 if you can’t see it.)
Answers
Answer:
C
Step-by-step explanation:
Answer:
D. 57 Square feet
Step-by-step explanation:
So first you do 4.5x2=9.0 then you times that by 2 so 9.0x2= 18
Next, you do 4.5x3= 13.5 then you times that by 2 so 13.5x2= 27
Lastly, you do 2x3 on one side and 2x3 on the other side. For both of those you get 6, so you do 6+6 and you get 12
Finally you do
18+27+12=57
Solve for x. Round your answer to the nearest tenth.
14.
х
11
X=
type your answer...
Answers
Answer:
8.7
Step-by-step explanation:
14² - 11² = x
196-121= 75
√75= 8.66
so rounding it would be 8.7
Then find the values of x and y.
Answers
Answer:
y = 4
x = 104°
Step-by-step explanation:
3y = y + 8
-y -y
2y÷2 = 8÷2
2y÷2 cancels out so
8 ÷ 2 = 4
y = 4
all sides are congruent so all angles are congruent so that means that all the angles are 104°